| WhyDoJournalistsLoveStupidEquations Recorded at the British Science Festival 2009l Keywords: Maths Downloads: 8 |

| maths_479 mathes reflection Keywords: maths Downloads: 17 |

| 9.1 Q 03 urdu Keywords: maths Downloads: 7 | |

| Theory of Probability- Convergence of Martingales. Fundamental Wald's Identity. - Dmitry Panchenko
Keywords: Maths Downloads: 28 | |

| Kinetic Theory- Linear Response - David Tong The goal of response theory is to �gure out how a system reacts to outside in�uences. These outside in�uences are things like applied electric and magnetic �elds, or applied pressure or an applied driving force due to some guy sticking a spoon into a quantum liquid and stirring. ... Keywords: Maths Downloads: 15 | |

| Classical and Quantum Chaos- Noise - Predrag Cvitanovi?;E.A. Spiegel This chapter (which reader can safely skip on the �rst reading) is about noise, how it a_ects classical dynamics, and the ways it mimics quantum dynamics. Keywords: Maths Downloads: 17 | |

| Optical Physics and Quantum Electronics- Plane Wave Propagation in a Linear, Homogeneous, Anisotropic Dielectric Media (Crystal Optics) - R. Victor Jones Our objective here is to formulate a general approach to the subject of wave propagation in anisotropic dielectrics which makes use of ideas familiar from other branches of mathematical physics -- viz. the �eigenvalue problem.�.18 For reasons that will soon become abundantly clear, treatments of �crystal optics� focus on the behavior of the dielectric displacement vector, r D (r r , _) rather than on the electric field vector.19 For non-magnetic dielectrics the components of the dielectr... Keywords: Maths Downloads: 14 | |

| Kinetic Theory- Kinetic Theory - David Tong The purpose of this section is to lay down the foundations of kinetic theory, starting from the Hamiltonian description of 10^23 particles, and ending with the Navier-Stokes equation of �uid dynamics. Our main tool in this task will be the Boltzmann equation.This will allow us to provide derivations of the transport properties that we sketched in the previous section, but without the more egregious inconsistencies that crept into our previous derivaion... Keywords: Maths Downloads: 22 | |

| Mathematics for Computer Science - Relations and Partial Orders - Albert R. Meyer A relation is a mathematical tool for describing associations between elements of sets. Relations are widely used in computer science, especially in databases and scheduling applications. A relation can be de�ned across many items in many sets, but in this text, we will focus on binary relations, which represent an association between two items in one or two sets. Keywords: Maths Downloads: 22 | |

| Mathematical Methods 3 - Jonny Evans This course is an introduction to some of the most ingenious ideas in 18th century mathematics. The course is divided into two parts. In the �rst part we will see how to turn some natural physical and geometric problems into di_erential equations. The second part of the course will develop techniques to solve some partial di_erential equations. Keywords: Maths Downloads: 60 | |

| Linear Partial Differential Equations Analysis and Numerics- The Heat and Wave Equations in 2D and 3D - Matthew Hancock We now consider the special case where the subregion D is the unit circle (we may assume the circle has radius 1 by choosing the length scale l for the spatial coordinates as the original radius): ... Keywords: Maths Downloads: 33 | |

| From Antiquity to Einstein- Lecture 6 - The Special Theory of Relativity - Nikos Drakos These notes cover the development of the current scienti�c concepts of space and time through history, emphasizing the newest developments and ideas.The presentation will be non-mathematical: the concepts will be introduced and explained, but no real calculations will be performed. The various concepts will be introduced in a historical order (whenever possible), this provides a measure of understanding as to how the ideas on which the modern theory of space and time is based were developed... Keywords: Maths Downloads: 18 | |

| General Relativity (Notes for Px436) - Tom Marsh These notes mostly show the essentials of the lectures, i.e. what I write on the board. The exception to the rule is when I write pieces of text like this (outside of the examples). These represent information that I may have said but not written during lectures. I use them when I think it would help you follow the notes. The notes are very terse, and brief to the point of grammatical inaccuracy.This is because they are notes and are not intended to replace books... Keywords: Maths Downloads: 15 | |

| Colliding Plane Waves in General Relativity- Chapter 18 - Colliding Electromagnetic Waves- Diagonal Solutions - Jerry Griffiths This chapter is a continuation of the review of all presently known exact solutions which describe the collision of plane electromagnetic waves, or a combination of both gravitational and electromagnetic waves. Attention is concentrated here only on diagonal solutions. These solutions may be considered as a generalization of the solutions representing the collision of gravitational waves with colinear aligned polarization that have been described in Chapter 10... Keywords: Maths Downloads: 16 | |

| Quantum Condensed Matter Field Theory- Lecture 7 - Quantum Magnetism and The Ferromagnetic Chain - Ben Simons Following on from our investigation of the phonon and interacting electron system, we now turn to another example involving bosonic degrees of freedom � the problem of quantum magnetism. Keywords: Maths Downloads: 15 | |

| Quantum Field Theory - Collated Notes - John W. Norbury Chapter 1. Lagrangian Field Theory 1.1 Units. We start with the most basic thing of all, namely units and concentrate on the units most widely used in particle physics and quantum �eld theory (natural units). We also mention the units used in General Relativity, because these days it is likely that students will study this subject as well. Keywords: Maths Downloads: 36 | |

| General Physics I- Thermal Physics 1 - Lawrence Evans;Mr. J. Edward Ladenburger In the following sections we will treat macroscopic systems that are in thermal equilibrium. Most of our discussion will center on the behavior of gases. We will use appropriate macroscopic variables, some of which are already familiar, such as density, volume and pressure. We will usually assume the CM of the system is at rest, and that molecular velocities are randomly distributed as to direction, so there is no bulk �ow or velocity �eld to consider... Keywords: Maths Downloads: 20 | |

| Thermal Energy- Part2C - Introduction to Thermochemistry - Zoltan Spakovszky In this section, we examine the issue of how we obtain the heat needed for work production. For the most part, this is from converting chemical energy into heat, so the discussion will be on reacting mixtures of gas which are involved in chemical combustion processes. The topic addressed is �thermochemistry�, which is the combining of thermodynamics with chemistry to predict such items as how much heat is released from a chemical reaction... Keywords: Maths Downloads: 29 | |

| Quantum Physics I- Lecture6 - Vladan Vuletic Photoelectric e_ect Observed 1888; explanation, Einstein 1905. A negatively charged metal plate loses charge slowly if illuminated with light, while a positive charge remains. Light of su_ciently short wavelength releases electrons, the electron current is proportional to the intensity of the light. Light below a certain cut o_ frequency _0 does not release any electrons, no matter how high the intensity... Keywords: Maths Downloads: 15 | |

| Complex Multiplication - James S. Milne These are preliminary notes for a modern account of the theory of complex multiplication. A shortened (minimal) version will be included in my book on Shimura varieties, and a complete longer version may one day be published separately. Keywords: Maths Downloads: 23 | |

| Groups and Symmetries - Frederique Oggier;Alfred Bruckstein These notes were designed to �t the syllabus of the course �Groups and Symmetries�, taught at Nanyang Technological University in autumn 2012, and 2013. Keywords: Maths Downloads: 50 | |

| Colliding Plane Waves in General Relativity- Chapter 8 - Singularity Structure - Jerry Griffiths It has been seen that singularities inevitably occur in the solutions describing the interaction region of colliding plane waves. Using the line element (6.20), we have in this region... Keywords: Maths Downloads: 13 | |

| Special Relativity - I - Elizabeth Stanway Objectives: (1) To recap some basic aspects of SR (2) To introduce important notation. Keywords: Maths Downloads: 10 | |

| Quantum Physics I- Lecture7 - Vladan Vuletic To develop some more insight into interference, and the correlations between quantum system and (classical) apparatus that lie at the heart of the quantum measurement problem, we will postulate rules on how the interference pattern is formed, and how photon scattering changes the electron�s wavefunction. Keywords: Maths Downloads: 18 | |

| Post-Newtonian Theory- Post-Newtonian Theory for The Common Reader - Eric Poisson
Keywords: Maths Downloads: 37 | |

| Relativity- Relativistic Dynamics - Max Tegmark Topics: Formula summary � Momentum & energy � Acceleration & force (optional) � Transformation of force (optional) � Transformation of acceleration (optional) Keywords: Maths Downloads: 25 | |

| General Physics II- Magnetostatics 1 - Mr. Travis Byington;Lawrence Evans;Mr. Ryan Magee;Hao Zhang We begin our discussion with magnetic �elds that are static, i.e., independent of time. The �eld is de�ned by its effect on a moving point charge. Then we discuss steady currents as sources of magnetic �elds, exploring some useful and important special con�gurations of currents. Later on we will discuss another important source of magnetic �elds, an electric �eld that is changing with time. Keywords: Maths Downloads: 15 | |

| Quantum Condensed Matter Field Theory- Lecture 21 - Cooper instability - Ben Simons In the �nal section of the course, we will explore a pairing instability of the electron gas which leads to condensate formation and the phenomenon of superconductivity. Keywords: Maths Downloads: 22 | |

| Theory of Probability- Martingales. Doob's Decomposition. Uniform Integrability. - Dmitry Panchenko
Keywords: Maths Downloads: 25 | |

| Theory of Probability- Laws of Large Numbers. - Dmitry Panchenko
Keywords: Maths Downloads: 12 | |

| Relativity- Relativistic Kinematics - Max Tegmark Topics: Lorentz transformations toolbox � � formula summary � inverse � composition (v addition) � boosts as rotations � the invariant � wave 4-vector � velocity 4-vector � aberration � Doppler e_ect � proper time under acceleration � calculus of variations � metrics, geodesics Implications� � Time dilation � Relativity of simultaneity, non-syncronization � Length contraction � c as universal speed limit � Rest length, proper time Keywords: Maths Downloads: 26 | |

| Colliding Plane Waves in General Relativity- Chapter 12 - Solution-Generating Techniques - Jerry Griffiths In this chapter we will consider only vacuum solutions. This will enable us to continue to concentrate on the collision of gravitational waves. Various techniques will be discussed here, and the main solutions that have been obtained using them will be described in the next chapter. Many techniques are also known by which solutions of the Einstein�Maxwell equations, and other non-vacuum solutions, can be generated from known vacuum solutions... Keywords: Maths Downloads: 11 | |

| Colliding Plane Waves in General Relativity- Chapter 6 - The Field Equations - Jerry Griffiths The colliding wave problem has been described in terms of two approaching waves in regions II and III, in a background region I, which is here taken to be �at. According to the work of Penrose (1980), the initial data are well set, so that a unique solution exists in the interaction region IV at least in the neighbourhood of the boundaries of regions II and III. It is therefore necessary �rst to state the relevant �eld equations in the interaction region, and then to attempt to solve them ... Keywords: Maths Downloads: 16 | |

| General Physics I- Thermal Physics 3 - Lawrence Evans;Mr. J. Edward Ladenburger
Keywords: Maths Downloads: 21 | |

| From Antiquity to Einstein- Lecture 8 - The Universe- Size, Origins, Contents - Nikos Drakos These notes cover the development of the current scienti�c concepts of space and time through history, emphasizing the newest developments and ideas.The presentation will be non-mathematical: the concepts will be introduced and explained, but no real calculations will be performed. The various concepts will be introduced in a historical order (whenever possible), this provides a measure of understanding as to how the ideas on which the modern theory of space and time is based were developed... Keywords: Maths Downloads: 21 | |

| Analytic Number Theory- 18.785- Primes in Arithmetic Progressions - Kiran S. Kedlaya In this unit, we �rst prove Dirichlet�s theorem on primes in arithmetic progressions. We then prove the prime number theorem in arithmetic progressions, modulo some exercises. Keywords: Maths Downloads: 23 | |

| Quantum Condensed Matter Field Theory- Lecture 16 - Applications and Connections - Ben Simons Partition Function of ideal (Non-Interacting) Gas of Quantum Particles Useful for �normalisation� of interacting theories Keywords: Maths Downloads: 12 | |

| Optical Physics and Quantum Electronics- Elementary Laser Models - Rate Equation Approach - R. Victor Jones Population Inversion and "Lasering" in a Three-Level System: Obviously, the trick in building masers and lasers has been to find means to "invert" the equilibrium population of states. First conceived by Charles Townes in 1951, Gordon, Zeiger and Townes in 1954... Keywords: Maths Downloads: 24 | |

| Colliding Plane Waves in General Relativity- - Introduction - Jerry Griffiths The subject to be discussed in this book is the collision and interaction of gravitational and electromagnetic waves. This is a particularly importanttopic in general relativity since the theory predicts that there will be a non-linear interaction between such waves. The e_ect of the non-linearity, however, is unclear. It is appropriate therefore to look in some detail at the simplest possible situation in which the e_ect of the non-linearity will be manifest: namely the interaction between coll... Keywords: Maths Downloads: 17 | |

| Differential Equations - Further Numerical Methods - John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
Keywords: Maths Downloads: 18 | |

| Thermal Energy- Part0 - Prelude- Review of Unified Engineering Thermodynamics - Zoltan Spakovszky
Keywords: Maths Downloads: 16 | |

| Introduction to Relativistic Quantum Chemistry- Chapter 3 - Relativistic Wave Equations - Pekka Pyykk� Klein-Gordon: The Schrodinger equation...contains �rst derivatives with respect to time, t, and second derivatives with respect to (xyz). We now wish to handle all four coordinates (x1x2x3x4) on equal footing. Keywords: Maths Downloads: 18 | |

| Mathematical Methods for Engineers II- One Fundamental Example - Gilbert Strang This chapter will have its own �avor, but it is strongly connected to the rest of this book. To make those connections, I want to begin with two speci�c examples. If you read even just this section, you will see the connections. Keywords: Maths Downloads: 16 | |

| Physics I- Classical Mechanics - Work and The Scalar Product - Peter Dourmashkin We shall introduce a vector operation, called the �dot product� or �scalar product� that takes any two vectors and generates a scalar quantity (a number). We shall see that the physical concept of work can be mathematically described by the dot product between the force and the displacement vectors. Keywords: Maths Downloads: 23 | |

| Physics I- Classical Mechanics - Conservation of Energy and Potential Energy - Peter Dourmashkin So far we have analyzed the motion of point-like bodies under the action of forces using Newton�s Laws of Motion. We shall now introduce the Principle of Conservation of Energy to study the changes in energy of a system between an initial state and final state. In particular we shall introduce the concept of potential energy to describe the effect of conservative internal forces acting on the constituent components of a system. Keywords: Maths Downloads: 22 | |

| Introduction to Partial Differential Equations - Class Meeting # 6- Laplace's and Poisson's Equations - Jared Speck We will now study the Laplace and Poisson equations on a domain (i.e. open connected subset) _ _ R^n Keywords: Maths Downloads: 12 | |

| Lectures on Quantum Field Theory - Lecture 6 - Quantum Electrodynamics - David Tong In this section we �nally get to quantum electrodynamics (QED), the theory of light interacting with charged matter. Our path to quantization will be as before: we start with the free theory of the electromagnetic �eld and see how the quantum theory gives rise to a photon with two polarization states. We then describe how to couple the photon to fermions and to bosons. Keywords: Maths Downloads: 16 | |

| Pages From Tcu 12 R 2 No description. Keywords: Maths Downloads: 47 | |

| Special Relativity - II - Elizabeth Stanway Objectives: Four vectors Keywords: Maths Downloads: 12 | |

| Seminar in Geometry- Chapter 16- Manifolds and Geodesics - Emma Carberry
Keywords: Maths Downloads: 12 | |